Exponential Attractors for Lattice Dynamical Systems in Weighted Spaces

Abstract

The aim of this paper is to investigate the existence of exponential attractors for lattice reaction-diffusion systems in weighted spaces $l_{\sigma}^{2}$ and for partly dissipative lattice reaction-diffusion systems in weighted spaces $l_{\mu}^{2}\times l_{\mu}^{2}$ , respectively. In contrast to the previous work by Abdallah in J. Math. Anal. Appl. 339, 217---224 (2008) and Commun. Pure Appl. Anal. 8, 803---818 (2009), we get the existence of exponential attractors for lattice dynamical systems in the weak topology spaces.